Zeitschrift für angewandte Mathematik und Physik最新文献

In this paper, we obtain the existence of a positive solution for a class of nonvariational fractional elliptic system with concave and convex nonlinearities in two cases. The paper is divided in two parts: In the first one, for general nonlinearity with subcritical or critical growth, we use Galerkin’s method and an approximation argument to show the existence of a solution for the system considered. In the second part, for special cases (which include the power case), we remove the restriction on the growth of the nonlinearity and use sub-supersolution, monotone iteration and a comparison argument to obtain a solution for the system considered.

In this article, a class of Caputo–Hadamard fractional stochastic differential equation (FSDEs) with time-delays and impulses is considered. With the help of contraction mapping principle, we derive the existence and uniqueness of the solutions to the purposed system. Subsequently, by virtue of the stochastic analysis techniques and generalized Gr(ddot{o})nwall inequality, the Ulam–Hyers stability (U–Hs) of the addressed system is established. Finally, we present an example to illustrate the theoretical results.

We analyze the spectral and dynamical stability of solitary wave solutions to the Lugiato–Lefever equation on (mathbb {R}). Our interest lies in solutions that arise through bifurcations from the phase-shifted bright soliton of the nonlinear Schrödinger equation. These solutions are highly nonlinear, localized, far-from-equilibrium waves, and are the physical relevant solutions to model Kerr frequency combs. We show that bifurcating solitary waves are spectrally stable when the phase angle satisfies (theta in (0,pi )), while unstable waves are found for angles (theta in (pi ,2pi )). Furthermore, we establish asymptotic orbital stability of spectrally stable solitary waves against localized perturbations. Our analysis exploits the Lyapunov–Schmidt reduction method, the instability index count developed for linear Hamiltonian systems, and resolvent estimates.

This study developed a novel nonlocal numerical model based on the peridynamic differential operator to analyze the thermoelectric coupling field. The thermoelectric coupling equations and boundary conditions are transformed from the classical partial differential form to the nonlocal integral form. By introducing the peridynamic function, a one-dimensional nonlocal model is established. This model can accurately capture the spatial distributions of the temperature field and material parameters when considering temperature-dependent thermoelectric material parameters. The numerical solutions from this nonlocal peridynamic model were found to agree well with those from the homotopy analysis method. Using this model, the influence of temperature boundary conditions and structure length on output performance is studied. The intrinsic relationship between the material parameters and the output properties within the structure is revealed. This presented nonlocal model provides an accurate mathematical tool to solve the thermoelectric coupling field for thermoelectric structures performance analysis.

In this paper, we study multi-bump solutions of the following Kirchhoff type equation:

where M is continuous with (inf _{mathbb {R}^+}M>0), (V ge 0) and its zero set has several disjoint bounded components, (mu ), (lambda ) are positive parameters, f has exponential critical growth. When V decays to zero at infinity, we use variational methods to obtain the existence and concentration behavior of multi-bump solutions.

A nonlocal diffusion single population model with advection and free boundaries is considered. Our aim is to discuss how the advection rate affects dynamic behaviors of species under the case of small advection. Firstly, the well-posed global solution is obtained. Secondly, we apply the eigenvalue problem of integro-differential operator to obtain the dichotomy and sharp criteria for spreading and vanishing, which is determined by initial habitat and initial density. Further, the asymptotic spreading speed of species is estimated when spreading happens. Namely, we get the exact asymptotic spreading speed and find that if kernel function satisfies the certain condition, then the leftward asymptotic spreading speed is less than the rightward one due to the impact of advection rate. Meanwhile, we also observe that accelerated spreading happens if the certain condition does not be satisfied.

This paper focuses on studying blow-up prevention by sub-logistic sources in 2D Keller–Segel chemotaxis systems with superlinear signal production. An application of a result on parabolic gradient regularity for parabolic equations in Orlicz spaces shows that the presence of sub-logistic sources is indeed sufficiently strong to ensure the global existence and boundedness of solutions. Our proof also relies on several techniques, including parabolic regularity in Sobolev spaces, variational arguments, interpolation inequalities in Sobolev spaces, and Moser iteration method.